The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Explanation

Let, the required number be x and y, where `xgty`
Given `x^(2)-y^(2)=180" ".....(1)`
and `y^(2)=8x" "......(2)`
From equation (1) and (2) we have
`x^(2)-8x=180`
`impliesx^(2)-8x-180=0impliesx^(2)-(18-10)x-180=0`
`impliesx^(2)-18x+10x-180=0impliesx(s-18)+10(x-18)=0`
`implies(x-18)(x+10)=0`
`impliesx=18orx=-10`
when `x=18impliesy^(2)=8xx18=144ory=+-12`
and when `x=-10impliesy^(2)=8xx-10=-80`
which is imaginary i.e., not possible.
Hence, numbers are (18 and 12) or (18 and -12).